A lot of things are possible and suitable with your wide array of interests. I'll just give you some random remarks and you can do with them what you like. :-)
- The Ardennes region in Belgium has kayaking, biking, rappelling/ climbing and other outdoor sports and activities. And war museums, beer breweries, impressive big caves you can visit with a guide (for example Remouchamps or Han), cute medieval towns such as Durbuy and Spa (but also very depressing ugly villages, just see the instagram account "ugly Belgian houses",... so always do a Google Streetview before deciding where you're staying). You would need a car for convenience in this region, public transport is not so frequent and dense.
- With children of that age, the type of holiday a lot of Dutch parents choose to do is to book a bungalow in one of the many bungalow parks like Landal, Eurocamps, Roompot and others (I would avoid the outdated and dirty CenterParcs). This has the big advantage of (usually) being in a nature area, having all kinds of playgrounds, a pool, organized activities for children (from baking pizzas or cookies to all kinds of creative or active sessions), free parking, a private bungalow with kitchen, private terrace and TV, and privacy at night for the parents, restaurant and little grocery store on site, and other children to play with of course. From there it's easy to make plans last-minute (dependent on your mood / the children's moods, the weather or whatever), for example visit nearby towns, museums, zoos / wildlife parks, special playgrounds, the beach / forest or whatever.
Personally I would not want to have a typical "grown-up" holiday doing museums and historical towns and seeing lots of "sights" with such young children who have completely different interests. It's nice to bring them along for an hour or two, for example to a museum, but I'm sure they also simply want playtime? I would google for specific places that are fun for both adults as well as children, for example Apenheul monkey zoo could be fun, or Beekse Bergen (the latter even has bungalows where you can stay and see giraffes from your window).
Various museums have special puzzle tours or other fun things for children but the 3 y/o may be super bored quickly, not understanding such things fully yet?
- If you happen to go southeast near Venlo / Arcen in the Netherlands: Irrland play park in Germany (just across the border near Arcen) is absolutely fantastic for kids under 12. It's much cheaper than Dutch play parks (€7.50 per person, as opposed to €38 and up for De Efteling in the Netherlands for example), it is huge, there is free parking, you are allowed to bring in your own food (unlike many other Dutch parks / zoos) and use the BBQ's in the park; or buy food / candy there; there are picnic tables next to everything that children can play on so that you can sit and relax and watch your child. There are tall slides, air pillows, rope towers, a corn "bath" to sit in and play with the corn, skelters, and lots more (mostly) non-electric playground equipment. There is also a small shallow stream that children love to play in when it's warm so bring towels and swimgear. You can rent a handkart to transport your stuff more easily (as said it is a huge park).
- Duinrell in Wassenaar near The Hague is a swimming pool with lots of spectacular slides and I believe there is also a bungalow park there. This could be a convenient location if you want to visit some bigger cities as a daytrip (by Dutch / Belgian norms, definitely tiny when compared to LA where you seem to be from!), such as The Hague, Delft, Leiden, Rotterdam, and Antwerp in Belgium. You could probably do so easily by public transport.
- If I were you I'd buy or borrow a Lonely Planet Netherlands and Belgium guidebook so that you have all the info about getting around (when are cars convenient, which public transport options are there), things to do in general (in all areas of these countries), and things to do for families, weather and climate, money issues, etc etc. They also offer itinerary suggestions.
- Of course you could decide to mix and match. Maybe a few nights in the crowded urbanized area in the west of the Netherlands first, and then rent a car and drive to the Ardennes in Belgium for some green time in the hills and forests and doing outdoor sports & games. Drive back to Rotterdam to drop the car off and get the ferry.
- Since you mentioned the ferry that makes me think you are not coming directly from LA but from the UK. Are you aware that there is also a very easy train connection from London to Brussels (in only 2 hours!)? Or all the way to Rotterdam / Amsterdam (only 4 hours for London - Amsterdam). See https://www.seat61.com/Belgium.htm and https://www.seat61.com/Netherlands.htm
Less polluting than the ferry too. ;-) And a lot faster from city center to city center than the 11 hour ferry ride (excluding the trip to Hull, and from the ferry terminal in Rotterdam to the center!).
For example you could take this train to Rotterdam, spend time in the western cities and smaller towns in the Netherlands, then take a train from Rotterdam to Brussels (optionally spending a few hours in Antwerp along the way as well), rent a car from there to visit the Ardennes region, drop the car off in Brussels, take the train directly from Brussels to London. Just an idea.
Good luck making choices out of the thousands of places of interest in these 2 countries. ;-)
